
The
The invention relates to a method for determining layer thicknesses
and optical parameters of a number of layers of a sample,
in which the reflection spectrum of the sample is measured and then smoothed,
and a modeled reflection spectrum is matched to the measured one
so as to determine the layer thicknesses, and refers to the problem
the determination of the thicknesses of multilayer systems.

Reflection spectrometry
is a longknown and widely used method of investigation
of layer systems, in particular of wafers, and for determination
the layer thicknesses and other optical parameters. The method is
very simple in principle: a sample that has several layers
has, is irradiated with light of a predetermined wavelength.
If the layers are transparent, the light penetrates into the media
and is in the transition areas
between two layers, including the transition between the uppermost
Layer and the surrounding atmosphere heard, partially reflected.
By overlay
incident and reflected light causes interference,
what the intensity
of the reflected light. The ratio of
intensities
of incident and reflected light determines the socalled
absolute reflectance, both intensities are therefore to be measured. varies
now the wavelength
in a given range continuously, you get that
Reflection spectrum, depending on
from the wavelength
Maxima and minima caused by the interference
become. The location of these extremes depends on the material properties
the sample which determines the optical behavior. To these optical
Counting parameters
for example refractive index and absorption coefficient. Farther
affected
the layer thickness the position of the extrema in the reflection spectrum.

Basically
it is possible
to deduce these parameters from the measured reflection spectrum; regarding
The thickness of the layers and their number are in an ideal
Model the limits very broad. The basic formulas
can be derived from the Fresnel diffraction theory,
as in the article "Polycrystalline
silicon film thickness measurement from analysis of visible reflectance spectra "by P. S. Hauge
in J. Opt. Soc. Am., Vol. 69 (8), 1979, pages 11431152
becomes. Like the book by O. Stenzel, "Das Dünnschichtspektrum", Akademieverlag
1996, pp. 77 to 80, the provision is designed
the optical constants and layer thicknesses by recalculation
in reality
However, very difficult and expensive, as the number of unknowns
is very big.

One is therefore dependent on approximations or must make restrictions. The easiest way to determine the thickness, if one limits the number of layers on a layer whose thickness is to be determined. In this case, a relationship between the layer thickness d and the refractive indices n (λ
_{i} ) for the wavelengths λ
_{i} belonging to extrema in the reflection spectrum can be established, the index i indicating the extrema. If the reflection spectrum contains a total number of m extremes between any two selected extrema λ
_{i} and λ
_{j} , then the layer thickness d can be calculated according to the equation
determine. However, in order to arrive at this expression, one has to make the limiting assumption of a weakly dispersive layer, with strong dispersion this formula fails, as well as with absorbent layers. This limits the class of materials that can be examined. Furthermore, it is assumed that the wavelengthdependent refractive index n (λ) is known. For example, this is based on the "Extrema method" in the scriptures
US 4,984,894 described method for determining the layer thickness of a layer.

In Scripture
US 5,440,141 A method for determining the thicknesses of three layers is described. An approximate thickness of the first layer is determined by the abovementioned "extrema method." In order to determine the exact thickness of the first layer, a modeled one is then modeled in a range of about ± 100 nm around this value for different thicknesses (i) And (ii) determines the deviations of the respectively modeled from the measured reflection spectrum These deviations are summarized in an error function E in which the deviations are received in quadratic form:
w
_{λ} is a weighting factor, R
^{ex is} the experimentally determined reflection spectrum, R
^{th is} the reflection spectrum modeled for a layer thickness. This function E dependent on the layer thickness is then minimized, ie the modeled reflection spectrum is sought where the deviations are smallest. The layer thickness at which the function E is minimal is identified as the actual layer thickness. In the case of multiple layers, however, this method can only be carried out if the first layer reflects in a first wavelength range in which the deeper layers absorb the light, so that they can be disregarded in the thickness determination of the first layer. In the cited document, reflection measurements are therefore carried out in two different wavelength ranges.

Around
determining an approximate thickness of the second layer
a frequency analysis of the reflection spectrum in the second wavelength range
carried out,
based on the fact that
Periodically repeat maxima and minima in the reflection spectrum,
what happens in the converted spectrum by the occurrence more or
less pronounced
Makes peaks noticeable. From these tips can be first approximatively on the thickness
infer the second layer. A
Approximate thickness of the third layer is provided by low pass filtering
Here, too, the different material properties
of the layer stack are exploited. In a similar way as for the thickness
the first layer becomes one of the thicknesses of the second and third
Layer dependent
Error function minimized, d. H. those thicknesses are sought for which the
Deviations from experimental and modeled reflection spectrum
are the smallest.

From the Scriptures
US 5,440,141 So it is clear that although the thicknesses of several layers can be determined, this works only for layer combinations of certain materials.

In Scripture
US 5,493,401 Finally, a method for determining the thicknesses of  in principle  any number of layers is described. First of all, the total number of extrema as well as the smallest and largest wavelength, which corresponds to an extremum, are determined. From these variables can be concluded that the total thickness of the layer stack, ie on the summed thicknesses of the individual layers. For different combinations of individual thicknesses, which add up to give the total thickness, a modeled reflection spectrum is then calculated in each case and an error function E similar to that described above is formed, which contains the deviations of the modeled from the experimental reflection spectrum. It is then sought that combination of thicknesses for which these deviations are the smallest.

However, the field of application is also in
US 5,493,401 limited method described. As soon as the experimental spectrum is changed more strongly by influences that are not or only insufficiently considered in the model, the results are no longer reliable, and one gets with high probability an incorrect set of layer thicknesses for which the function E assumes a local minimum. Light scattering, as z. B. occurs in polysilicon, and roughness of the sample surface affect z. For example, the expression of extremes  with strong roughness and high light scattering some extremes will be less pronounced, ie have a lower re flexionsgrad than actually predicted in the model. Also, an insufficient spectral resolution of the spectrometer can cause changes. Furthermore, the materials must be known because the refractive indices are given, as well as the absorption constants. Also changing to the expression of the extrema are pronounced strong dispersion or absorption. In particular, in the UV range, where the absorption is high, there may be deviations between modeled and experimental reflection spectrum, which is why the in the Scriptures
US 5,493,401 also preferably used at wavelengths in the range of 400 to 800 nm.

These
Factors that can change the experimental reflection spectrum become
in all theoretical models reflecting the different evaluation methods
not or only insufficiently taken into account. The bigger the
Deviations from the modeled and measured reflection spectrum are,
the bigger it gets
the uncertainty in finding a minimum of error function,
d. H. in determining the optimum layer thicknesses, and under
circumstances
beats
this search completely failed. This has led, among other things, that depending on
Sample system a particular, adapted model is used, what
for special
Material combinations provides acceptable results, but at
other sample systems failed.

Based on this prior art, the present invention seeks to provide a method develop with which the optical parameters and thicknesses of multilayer systems can be determined more reliably than before and which are less sensitive to disturbing factors that influence the reflection spectrum.

According to the invention in a method of the type described above, comprising in a first step, the introduction of a sample with a number N layers whose thicknesses are to be determined in a measuring arrangement and the measurement of the reflection spectrum of the sample in a predetermined wavelength range, in one second step, the smoothing of the measured reflection spectrum by reducing noise caused largely by external influences, in a third step, the selection of a set S _{1} of a number M, according to the size of ordered wavelengths λ _{1, i} , where i = 1, .. ., M, wherein each one wavelength λ _{1, i} in the set S _{1} corresponds in each case to a local extremum in the smoothed reflection spectrum, and the selection is made under the condition that two adjacent extremes differ by at least one predetermined contrast criterion, and the one the two extremes have a minimum, the other a maximum, in a fourth Stepwise fitting a modeled reflection spectrum to the smoothed reflection spectrum for the number N of layers by means of a model, which layer thicknesses or layer thicknesses and optical parameters are given as variable quantities, wherein in each adaptation step a set S _{2} of a number M, in the in the same way as in the set S _{1} ordered wavelengths λ _{2, j} , with j = 1, ..., M, is selected, each one wavelength λ _{2, j} in the set S _{2} each to a local extremum in the modeled reflection spectrum The selection is made on the condition that, of two adjacent extrema, one is a minimum, the other a maximum, and in each adjustment step, an optimization criterion is further determined, the best fit corresponding to a minimum of the optimization criterion, and so on Layer thicknesses can be substantially determined, achieved by the Optimi erungskriterium by the totality of the amounts of the wavelength differences of all pairs of wavelengths (λ _{1, i} , λ _{2, i} ), with i = 1, ..., M, is determined.

The
new process is based on the startling finding that it is sufficient
The location of the extrema in the model to the location of the extrema in the experimental
Spectrum to perform an accurate layer thickness determination
can.
The totality of the differences of the pairs of wavelengths is the
decisive criterion. To avoid having positive and negative differences
possibly each other
pick up and deliver a wrong set of layer thicknesses, considered
one the amount.

Prefers
Consider the sum of the squares of the differences, because provided
The optimization with the help of a computer system is supposed to happen
less arithmetic operations needed in this case than when considering the
Amount. But other functions, in each case the differences
the pairs of wavelengths
come in as an amount, are conceivable, for. B. polynomial functions.

at
a big one
Number of extremes and a high number of investigators
Samples continue to be cheap,
to weight the sum with the number M of extremes, this can then
at the same time to assess the quality of the adaptation for different
Samples are used.

Thereby,
that in the
inventive method
only the wavelengths,
but not  like
in the methods used so far  compared the reflection spectra
the new process is less dependent on disturbing influences. If
and how reflections are damped
are affected
the result therefore not, if they can be measured and
in the smoothed
Reflection spectrum are present. Also wavelengths where the degree of absorption
the sample is so high that the
Extremes strongly dampened
but are registrable, can be used for examination
become. Materials whose investigation with the previous methods
not or only with difficulty possible
was, are the inventive method
also easily accessible,
such as polysilicon, which due to the many different
Crystal directions has a high light scattering. Furthermore is
the analysis of thick layers is possible without any problems. With the new method
can be investigated layers of up to 50 microns thick. in principle
systems with many layers are also accessible to the process,
however, fitting in more than seven layers becomes very time consuming,
if you currently usual
Home computer used for evaluation and customization.

One
Another advantage of the method is that also determines optical parameters
you can, man
can also investigate layer systems of unknown materials.

The invention will be explained below with reference to an embodiment. In the dazuge showing impaired drawings

1 the basic structure of a measuring arrangement with sample,

2 the model of a sample,

3 Measured and modeled reflection spectrum for a sample 2 ,

In
1 is shown a possible arrangement, as it can be used in principle for determining layer thickness and in the prior art, for. B. in the Scriptures
DE 100 21 379 A1 is described. A sample
1 , for example a wafer, is introduced into the measuring system. In
1 the sample is in a holder
2 fixed. From a light source
3 A light beam L goes out via a beam splitter
4 is split into a reference beam R and a measuring beam M. About a lens
5 will be the sample
1 illuminated with the measuring beam M. The arrows and lines are intended to illustrate the light path. As a light source
3 For example, can serve a white light source, but also coherent light sources, such as lasers with tunable wavelength, are conceivable. Also, light sources that emit wavelengths in the optical range that can not be registered directly by the eye are included. By means of the beam splitter
4 It is possible, on the one hand, the direct signal of the light source and on the other hand, that of the sample
1 reflected light in a receiving unit
6 to register. The coupling of the reference light beam R and the measuring light beam L in the receiving unit
6 can, for example, with light guides
7 happen. In the receiving unit
6 becomes the light, if from the light source
3 several wavelengths at the same time, spectrally decomposed, and the intensities of the directincident and the reflected light are registered for each measured wavelength. The receiving unit
6 is with an evaluation unit
8th in which it is z. B. may be a commercial home computer, connected.

For example, the sample may be a layered system as described in U.S. Pat 2 outlined. On a silicon substrate, a lightinsensitive cover layer, a socalled photoresist layer is applied, whose thickness should be according to the manufacturer 6 microns. From which materials this layer is composed, plays no role in this method, in particular the optical material properties need not necessarily be known. Above the photoresist layer is air.

After the introduction of the sample 1 In the measuring arrangement, the reflection spectrum is measured in a predetermined wavelength range. The wavelength range may be limited to the area directly perceptible to the eye, but depending on the material system to be examined, it may also be necessary to take smaller or larger wavelengths into account as well.

That with a in 2 The reflection spectrum measured in the sample shown is in 3 shown as a black line. Especially in the wavelength range between 400 and 470 nm, the spectrum is considerably noisy, which is due to the measuring device. A smoothing process smooths the measured reflection spectrum, ie it reduces the noise caused by external influences. A common smoothing method which can be used here is, for example, a convolution of the reflection spectrum with a Gaussian function, another example method is the socalled "floating average method." Care must be taken, however, that the oscillations in the spectrum, which are the have steepest ascents or descents and originate from the thickest layers in the layer system, are not attenuated so much that they are not discarded in the next step of the process because they differ by less than one contrast criterion after smoothing The strongly noisy region between 430 and 470 nm can also be used for spectral analysis.

From the smoothed reflection spectrum, a set S _{1} of a number M wavelengths λ _{1, i} , with i = 1,..., M, is then selected. The selection is started on one side of the spectrum, for example on the longwave end of the recorded spectrum, and is terminated on the other side of the spectrum, so that the selected wavelengths λ _{1, i} are ordered by size. To select a wavelength λ _{1, i} three conditions must be met: (i) the wavelength λ _{1, i} must correspond to a local extre mum in the smoothed reflection spectrum, (ii) two adjacent extrema must differ by at least one predetermined contrast criterion, iii) and for two adjacent extrema one must be a minimum and the other a maximum. By specifying a contrast criterion, even existing noise is further reduced after smoothing, or extrema not caused by the layer structure is sorted out. The contrast criterion corresponds to a minimum difference in reflectance for every two adjacent extremes corresponding to the condition mentioned in (iii), which must be exceeded in order to select the smaller of the two wavelengths, provided one chooses the wavelengths long wavy end of the spectrum begins. For example, as a contrast criterion, it may be required that the extrema must differ by at least 4% of the maximum value in the reflection spectrum.

Around
To determine the layer thicknesses and other optical parameters, one must one
Model based, calculated by means of which a reflection spectrum
can be. There are different models in the literature
offered, with some models known refractive and absorption indices
presuppose, as the methods mentioned at the beginning. In the method according to the invention
But especially those models can be used
not only the layer thicknesses but also optical parameters,
like refractive and absorption indices, as variables of variation.

With the aid of such a model, a reflection spectrum can then be modeled for a given number N of layers and adapted stepwise to the smoothed reflection spectrum. This can be done, for example, at the evaluation unit 8th be performed. In the process, a reflection spectrum is modeled for different combinations of parameters, which enter as variable variables.

For each modeled reflection spectrum, a set S _{2} of a number M wavelengths λ _{2, j} , with i = 1,..., M is then also selected, in analogy to the measured and smoothed reflection spectrum. In this case, the selection is started on the same side of the spectrum on which the selection for the set S _{1 has} started, so that the selected wavelengths λ _{2, i are ordered} in the same way as in the set S _{1} . The selection is again made under the condition that of two adjacent extrema, one is a minimum and the other is a maximum.

Thus, a set S
_{2} contains as many wavelengths as the set S
_{1} , and two wavelengths λ
_{1, i} and λ
_{2, i} with the same index i correspond in each case to the extremes in the smoothed or modeled reflection spectrum. which are considered to belong to the same reflexes. For each modeled reflection spectrum, an optimization criterion is determined. The best fit is achieved when the optimization criterion takes a minimum. The optimization criterion can be represented according to the invention, for example, by the following function:

Q _{opt} designates the optimization criterion, and {P _{j} } represents the set of parameters that enter the model of the reflection spectrum as variable quantities; the running index j assumes all values between 1 and the maximum number of incoming parameters. In the optimization criterion thus enter the differences of pairs (λ _{1, i} λ _{2, i} ) in each case corresponding wavelengths.

at
There are many ways of determining the minimum of the optimization criterion
various possibilities,
two of which are mentioned here by way of example in order to clarify the discovery process.

In the first possibility, a definition range is first defined for each parameter which enters the model of the reflection spectrum as a variable variable, ie the parameters can each lie between a predetermined minimum and maximum value. Between these limits, a number of values are set at approximately constant intervals for each parameter. This results in a number of combinations of parameters, and in each adaptation step, a reflection spectrum is modeled for one of these combinations, the optimization criterion is determined and compared with the optimization criterion of the combination of parameters that has hitherto provided the minimum. If it returns a smaller value, the previous combination is discarded and the optimization criterion calculated in this step is defined as a new minimum. The combination of parameters that yields the new minimum is stored as an optimal combination of parameters, for example, in a memory located in the evaluation unit 8th can be located. Since no optimization criterion from a previous step is present in the first adaptation step, it makes sense to allocate a very large value, eg. B. 10 ^{20} , the optimization criterion. This value is generally fallen below immediately in the first adaptation step.

In this way, of all possible combinations of parameters, one can find those whose optimization criterion is minimal in comparison with the others and which therefore comes closest to the actual parameters. With this method, it is very easy to study the global minimum, or at least the area in the vicinity of this minimum, in an accuracy that is approximately equal to the distance between two examined values of a parameter, since one examines parameter combinations over a large range of parameter combinations ters, find.

When
second option
let yourself
a more accurate determination of the minimum using standardized mathematical
Algorithms, such. B. the method of conjugated gradients,
to reach. Here, however, a prerequisite is that of a parameter combination
which comes very close to the global minimum,
otherwise there is a risk of finding a local minimum. moreover
this method is very time consuming. For this reason, it is recommended
first
to narrow the area in which the assumed global minimum lies,
for example, with the method mentioned as a first option
and the combination of parameters found there
as output combination for
to use the gradient method.

To increase the layer thickness of the photoresist layer of the in 2 To determine the system shown, this combination of the two options was used. Variable sizes are the layer thickness of the photoresist layer and its refractive index. The reflection spectrum, whose optimization criterion yields a minimum, is in 3 shown as a gray line. The layer thickness results in a value of 6149 nm. This again clearly shows an advantage of the method according to the invention in that also optical parameters can be determined.

 1
 sample
 2
 bracket
 3
 light source
 4
 beamsplitter
 5
 lens
 6
 receiver unit
 7
 light pipes
 8th
 evaluation
 L
 ray of light
 R
 reference beam
 M
 measuring beam